LMFDB - Embedded newform 210.3.e.a.71.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(71,210)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("210.71");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 34 x^{14} - 80 x^{13} + 97 x^{12} - 80 x^{11} + 498 x^{10} - 3288 x^{9} + \cdots + 43046721 $ x^16 - 8x^15 + 34x^14 - 80x^13 + 97x^12 - 80x^11 + 498x^10 - 3288x^9 + 11844x^8 - 29592x^7 + 40338x^6 - 58320x^5 + 636417x^4 - 4723920x^3 + 18068994x^2 - 38263752*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.12
Root			$1.51079 - 2.59182i$ of defining polynomial
Character	$\chi$	$=$	210.71
Dual form			210.3.e.a.71.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-1.51079 + 2.59182i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.66538 - 2.13658i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(-4.43502 - 7.83139i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-1.51079 + 2.59182i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.66538 - 2.13658i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(-4.43502 - 7.83139i) q^{9} -3.16228 q^{10} +14.6732i q^{11} +(3.02158 - 5.18363i) q^{12} -19.1112 q^{13} -3.74166i q^{14} +(-5.79548 - 3.37823i) q^{15} +4.00000 q^{16} -29.7911i q^{17} +(11.0753 - 6.27207i) q^{18} +14.7237 q^{19} -4.47214i q^{20} +(3.99718 - 6.85730i) q^{21} -20.7510 q^{22} -22.7912i q^{23} +(7.33076 + 4.27316i) q^{24} -5.00000 q^{25} -27.0273i q^{26} +(26.9979 + 0.336829i) q^{27} +5.29150 q^{28} +51.5923i q^{29} +(4.77754 - 8.19604i) q^{30} -38.6980 q^{31} +5.65685i q^{32} +(-38.0302 - 22.1681i) q^{33} +42.1310 q^{34} -5.91608i q^{35} +(8.87004 + 15.6628i) q^{36} -29.2081 q^{37} +20.8224i q^{38} +(28.8731 - 49.5328i) q^{39} +6.32456 q^{40} +28.6850i q^{41} +(9.69769 + 5.65286i) q^{42} -40.4802 q^{43} -29.3464i q^{44} +(17.5115 - 9.91701i) q^{45} +32.2317 q^{46} +10.5901i q^{47} +(-6.04316 + 10.3673i) q^{48} +7.00000 q^{49} -7.07107i q^{50} +(77.2131 + 45.0082i) q^{51} +38.2224 q^{52} +95.5975i q^{53} +(-0.476348 + 38.1808i) q^{54} -32.8102 q^{55} +7.48331i q^{56} +(-22.2444 + 38.1611i) q^{57} -72.9625 q^{58} -11.1354i q^{59} +(11.5910 + 6.75646i) q^{60} -104.131 q^{61} -54.7273i q^{62} +(11.7340 + 20.7199i) q^{63} -8.00000 q^{64} -42.7340i q^{65} +(31.3504 - 53.7828i) q^{66} +45.2575 q^{67} +59.5823i q^{68} +(59.0707 + 34.4328i) q^{69} +8.36660 q^{70} +93.7964i q^{71} +(-22.1505 + 12.5441i) q^{72} -62.8141 q^{73} -41.3066i q^{74} +(7.55396 - 12.9591i) q^{75} -29.4474 q^{76} -38.8216i q^{77} +(70.0499 + 40.8327i) q^{78} +122.486 q^{79} +8.94427i q^{80} +(-41.6612 + 69.4647i) q^{81} -40.5668 q^{82} +68.2772i q^{83} +(-7.99435 + 13.7146i) q^{84} +66.6150 q^{85} -57.2477i q^{86} +(-133.718 - 77.9452i) q^{87} +41.5020 q^{88} -79.4213i q^{89} +(14.0248 + 24.7650i) q^{90} +50.5635 q^{91} +45.5825i q^{92} +(58.4647 - 100.298i) q^{93} -14.9766 q^{94} +32.9231i q^{95} +(-14.6615 - 8.54632i) q^{96} -28.2049 q^{97} +9.89949i q^{98} +(114.911 - 65.0759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9	$ 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9} + 16 q^{12} - 20 q^{15} + 64 q^{16} - 32 q^{18} + 48 q^{19} + 28 q^{21} - 96 q^{22} - 32 q^{24} - 80 q^{25} + 64 q^{27} - 88 q^{33} + 160 q^{34} + 8 q^{36} + 80 q^{37} + 156 q^{39} - 336 q^{43} - 80 q^{45} + 32 q^{46} - 32 q^{48} + 112 q^{49} + 84 q^{51} - 32 q^{54} - 80 q^{55} - 264 q^{57} + 96 q^{58} + 40 q^{60} + 112 q^{61} + 112 q^{63} - 128 q^{64} + 240 q^{67} + 8 q^{69} + 64 q^{72} + 48 q^{73} + 40 q^{75} - 96 q^{76} + 208 q^{78} + 8 q^{79} - 124 q^{81} - 608 q^{82} - 56 q^{84} + 120 q^{85} - 120 q^{87} + 192 q^{88} + 160 q^{90} - 56 q^{91} + 104 q^{93} + 32 q^{94} + 64 q^{96} - 192 q^{97} - 52 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9 + 16 * q^12 - 20 * q^15 + 64 * q^16 - 32 * q^18 + 48 * q^19 + 28 * q^21 - 96 * q^22 - 32 * q^24 - 80 * q^25 + 64 * q^27 - 88 * q^33 + 160 * q^34 + 8 * q^36 + 80 * q^37 + 156 * q^39 - 336 * q^43 - 80 * q^45 + 32 * q^46 - 32 * q^48 + 112 * q^49 + 84 * q^51 - 32 * q^54 - 80 * q^55 - 264 * q^57 + 96 * q^58 + 40 * q^60 + 112 * q^61 + 112 * q^63 - 128 * q^64 + 240 * q^67 + 8 * q^69 + 64 * q^72 + 48 * q^73 + 40 * q^75 - 96 * q^76 + 208 * q^78 + 8 * q^79 - 124 * q^81 - 608 * q^82 - 56 * q^84 + 120 * q^85 - 120 * q^87 + 192 * q^88 + 160 * q^90 - 56 * q^91 + 104 * q^93 + 32 * q^94 + 64 * q^96 - 192 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−1.51079	+	2.59182i	−0.503597	+	0.863939i
$3$	−1.51079	+	2.59182i	−0.503597	+	0.863939i
$4$	−2.00000			−0.500000
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	−3.66538	−	2.13658i	−0.610897	−	0.356097i
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		−	2.82843i		−	0.353553i
$9$	−4.43502	−	7.83139i	−0.492780	−	0.870154i
$10$	−3.16228			−0.316228
$11$			14.6732i			1.33393i	0.745091	+	0.666963i	$0.232406\pi$
$11$			14.6732i			1.33393i	−0.745091	+	0.666963i	$0.767594\pi$
$12$	3.02158	−	5.18363i	0.251799	−	0.431969i
$13$	−19.1112			−1.47009			−0.735047	−	0.678016i	$-0.762840\pi$
$13$	−19.1112			−1.47009			−0.735047	+	0.678016i	$0.762840\pi$
$14$		−	3.74166i		−	0.267261i
$15$	−5.79548	−	3.37823i	−0.386365	−	0.225215i
$16$	4.00000			0.250000
$17$		−	29.7911i		−	1.75242i	−0.481930	−	0.876210i	$-0.660064\pi$
$17$		−	29.7911i		−	1.75242i	0.481930	−	0.876210i	$-0.339936\pi$
$18$	11.0753	−	6.27207i	0.615292	−	0.348448i
$19$	14.7237			0.774930			0.387465	−	0.921884i	$-0.373351\pi$
$19$	14.7237			0.774930			0.387465	+	0.921884i	$0.373351\pi$
$20$		−	4.47214i		−	0.223607i
$21$	3.99718	−	6.85730i	0.190342	−	0.326538i
$22$	−20.7510			−0.943228
$23$		−	22.7912i		−	0.990924i	−0.868630	−	0.495462i	$-0.834999\pi$
$23$		−	22.7912i		−	0.990924i	0.868630	−	0.495462i	$-0.165001\pi$
$24$	7.33076	+	4.27316i	0.305448	+	0.178048i
$25$	−5.00000			−0.200000
$26$		−	27.0273i		−	1.03951i
$27$	26.9979	+	0.336829i	0.999922	+	0.0124751i
$28$	5.29150			0.188982
$29$			51.5923i			1.77904i	0.456891	+	0.889522i	$0.348963\pi$
$29$			51.5923i			1.77904i	−0.456891	+	0.889522i	$0.651037\pi$
$30$	4.77754	−	8.19604i	0.159251	−	0.273201i
$31$	−38.6980			−1.24832			−0.624162	−	0.781295i	$-0.714560\pi$
$31$	−38.6980			−1.24832			−0.624162	+	0.781295i	$0.714560\pi$
$32$			5.65685i			0.176777i
$33$	−38.0302	−	22.1681i	−1.15243	−	0.671761i
$34$	42.1310			1.23915
$35$		−	5.91608i		−	0.169031i
$36$	8.87004	+	15.6628i	0.246390	+	0.435077i
$37$	−29.2081			−0.789409			−0.394705	−	0.918808i	$-0.629153\pi$
$37$	−29.2081			−0.789409			−0.394705	+	0.918808i	$0.629153\pi$
$38$			20.8224i			0.547959i
$39$	28.8731	−	49.5328i	0.740335	−	1.27007i
$40$	6.32456			0.158114
$41$			28.6850i			0.699635i	0.936818	+	0.349817i	$0.113756\pi$
$41$			28.6850i			0.699635i	−0.936818	+	0.349817i	$0.886244\pi$
$42$	9.69769	+	5.65286i	0.230897	+	0.134592i
$43$	−40.4802			−0.941400			−0.470700	−	0.882293i	$-0.655999\pi$
$43$	−40.4802			−0.941400			−0.470700	+	0.882293i	$0.655999\pi$
$44$		−	29.3464i		−	0.666963i
$45$	17.5115	−	9.91701i	0.389145	−	0.220378i
$46$	32.2317			0.700689
$47$			10.5901i			0.225321i	0.993634	+	0.112660i	$0.0359372\pi$
$47$			10.5901i			0.225321i	−0.993634	+	0.112660i	$0.964063\pi$
$48$	−6.04316	+	10.3673i	−0.125899	+	0.215985i
$49$	7.00000			0.142857
$50$		−	7.07107i		−	0.141421i
$51$	77.2131	+	45.0082i	1.51398	+	0.882513i
$52$	38.2224			0.735047
$53$			95.5975i			1.80373i	0.432022	+	0.901863i	$0.357800\pi$
$53$			95.5975i			1.80373i	−0.432022	+	0.901863i	$0.642200\pi$
$54$	−0.476348	+	38.1808i	−0.00882126	+	0.707052i
$55$	−32.8102			−0.596550
$56$			7.48331i			0.133631i
$57$	−22.2444	+	38.1611i	−0.390253	+	0.669492i
$58$	−72.9625			−1.25797
$59$		−	11.1354i		−	0.188735i	−0.995537	−	0.0943675i	$-0.969917\pi$
$59$		−	11.1354i		−	0.188735i	0.995537	−	0.0943675i	$-0.0300829\pi$
$60$	11.5910	+	6.75646i	0.193183	+	0.112608i
$61$	−104.131			−1.70707			−0.853533	−	0.521038i	$-0.825545\pi$
$61$	−104.131			−1.70707			−0.853533	+	0.521038i	$0.825545\pi$
$62$		−	54.7273i		−	0.882698i
$63$	11.7340	+	20.7199i	0.186253	+	0.328887i
$64$	−8.00000			−0.125000
$65$		−	42.7340i		−	0.657446i
$66$	31.3504	−	53.7828i	0.475007	−	0.814891i
$67$	45.2575			0.675486			0.337743	−	0.941238i	$-0.390337\pi$
$67$	45.2575			0.675486			0.337743	+	0.941238i	$0.390337\pi$
$68$			59.5823i			0.876210i
$69$	59.0707	+	34.4328i	0.856097	+	0.499026i
$70$	8.36660			0.119523
$71$			93.7964i			1.32108i	0.750792	+	0.660538i	$0.229672\pi$
$71$			93.7964i			1.32108i	−0.750792	+	0.660538i	$0.770328\pi$
$72$	−22.1505	+	12.5441i	−0.307646	+	0.174224i
$73$	−62.8141			−0.860468			−0.430234	−	0.902717i	$-0.641569\pi$
$73$	−62.8141			−0.860468			−0.430234	+	0.902717i	$0.641569\pi$
$74$		−	41.3066i		−	0.558197i
$75$	7.55396	−	12.9591i	0.100719	−	0.172788i
$76$	−29.4474			−0.387465
$77$		−	38.8216i		−	0.504176i
$78$	70.0499	+	40.8327i	0.898076	+	0.523496i
$79$	122.486			1.55046			0.775231	−	0.631678i	$-0.217634\pi$
$79$	122.486			1.55046			0.775231	+	0.631678i	$0.217634\pi$
$80$			8.94427i			0.111803i
$81$	−41.6612	+	69.4647i	−0.514336	+	0.857589i
$82$	−40.5668			−0.494717
$83$			68.2772i			0.822617i	0.911496	+	0.411309i	$0.134928\pi$
$83$			68.2772i			0.822617i	−0.911496	+	0.411309i	$0.865072\pi$
$84$	−7.99435	+	13.7146i	−0.0951709	+	0.163269i
$85$	66.6150			0.783706
$86$		−	57.2477i		−	0.665671i
$87$	−133.718	−	77.9452i	−1.53699	−	0.895922i
$88$	41.5020			0.471614
$89$		−	79.4213i		−	0.892374i	−0.894940	−	0.446187i	$-0.852782\pi$
$89$		−	79.4213i		−	0.892374i	0.894940	−	0.446187i	$-0.147218\pi$
$90$	14.0248	+	24.7650i	0.155831	+	0.275167i
$91$	50.5635			0.555643
$92$			45.5825i			0.495462i
$93$	58.4647	−	100.298i	0.628652	−	1.07848i
$94$	−14.9766			−0.159326
$95$			32.9231i			0.346559i
$96$	−14.6615	−	8.54632i	−0.152724	−	0.0890242i
$97$	−28.2049			−0.290773			−0.145386	−	0.989375i	$-0.546442\pi$
$97$	−28.2049			−0.290773			−0.145386	+	0.989375i	$0.546442\pi$
$98$			9.89949i			0.101015i
$99$	114.911	−	65.0759i	1.16072	−	0.657332i
$100$	10.0000			0.100000
$101$			10.6769i			0.105712i	0.998602	+	0.0528561i	$0.0168324\pi$
$101$			10.6769i			0.105712i	−0.998602	+	0.0528561i	$0.983168\pi$
$102$	−63.6512	+	109.196i	−0.624031	+	1.07055i
$103$	34.1042			0.331109			0.165554	−	0.986201i	$-0.447059\pi$
$103$	34.1042			0.331109			0.165554	+	0.986201i	$0.447059\pi$
$104$			54.0547i			0.519757i
$105$	15.3334	+	8.93796i	0.146032	+	0.0851234i
$106$	−135.195			−1.27543
$107$			15.4338i			0.144241i	0.997396	+	0.0721205i	$0.0229766\pi$
$107$			15.4338i			0.144241i	−0.997396	+	0.0721205i	$0.977023\pi$
$108$	−53.9958	−	0.673658i	−0.499961	−	0.00623757i
$109$	−31.7494			−0.291278			−0.145639	−	0.989338i	$-0.546524\pi$
$109$	−31.7494			−0.291278			−0.145639	+	0.989338i	$0.546524\pi$
$110$		−	46.4007i		−	0.421824i
$111$	44.1274	−	75.7021i	0.397544	−	0.682001i
$112$	−10.5830			−0.0944911
$113$			26.1742i			0.231630i	0.993271	+	0.115815i	$0.0369480\pi$
$113$			26.1742i			0.231630i	−0.993271	+	0.115815i	$0.963052\pi$
$114$	−53.9679	−	31.4583i	−0.473403	−	0.275950i
$115$	50.9628			0.443155
$116$		−	103.185i		−	0.889522i
$117$	84.7587	+	149.667i	0.724433	+	1.27921i
$118$	15.7478			0.133456
$119$			78.8199i			0.662352i
$120$	−9.55508	+	16.3921i	−0.0796257	+	0.136601i
$121$	−94.3023			−0.779358
$122$		−	147.264i		−	1.20708i
$123$	−74.3463	−	43.3371i	−0.604442	−	0.352334i
$124$	77.3961			0.624162
$125$		−	11.1803i		−	0.0894427i
$126$	−29.3024	+	16.5943i	−0.232558	+	0.131701i
$127$	155.334			1.22311			0.611553	−	0.791204i	$-0.290545\pi$
$127$	155.334			1.22311			0.611553	+	0.791204i	$0.290545\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	61.1572	−	104.917i	0.474086	−	0.813312i
$130$	60.4350			0.464885
$131$		−	100.859i		−	0.769912i	−0.922935	−	0.384956i	$-0.874217\pi$
$131$		−	100.859i		−	0.769912i	0.922935	−	0.384956i	$-0.125783\pi$
$132$	76.0604	+	44.3362i	0.576215	+	0.335880i
$133$	−38.9552			−0.292896
$134$			64.0038i			0.477640i
$135$	−0.753172	+	60.3691i	−0.00557905	+	0.447179i
$136$	−84.2620			−0.619574
$137$		−	117.672i		−	0.858920i	−0.903086	−	0.429460i	$-0.858704\pi$
$137$		−	117.672i		−	0.858920i	0.903086	−	0.429460i	$-0.141296\pi$
$138$	−48.6953	+	83.5386i	−0.352865	+	0.605352i
$139$	−74.8843			−0.538736			−0.269368	−	0.963037i	$-0.586815\pi$
$139$	−74.8843			−0.538736			−0.269368	+	0.963037i	$0.586815\pi$
$140$			11.8322i			0.0845154i
$141$	−27.4475	−	15.9994i	−0.194663	−	0.113471i
$142$	−132.648			−0.934142
$143$		−	280.422i		−	1.96100i
$144$	−17.7401	−	31.3255i	−0.123195	−	0.217538i
$145$	−115.364			−0.795613
$146$		−	88.8326i		−	0.608443i
$147$	−10.5755	+	18.1427i	−0.0719424	+	0.123420i
$148$	58.4163			0.394705
$149$		−	149.584i		−	1.00392i	−0.864891	−	0.501960i	$-0.832612\pi$
$149$		−	149.584i		−	1.00392i	0.864891	−	0.501960i	$-0.167388\pi$
$150$	18.3269	+	10.6829i	0.122179	+	0.0712194i
$151$	202.607			1.34177			0.670884	−	0.741562i	$-0.265915\pi$
$151$	202.607			1.34177			0.670884	+	0.741562i	$0.265915\pi$
$152$		−	41.6449i		−	0.273979i
$153$	−233.306	+	132.124i	−1.52487	+	0.863557i
$154$	54.9020			0.356507
$155$		−	86.5315i		−	0.558268i
$156$	−57.7461	+	99.0655i	−0.370167	+	0.635036i
$157$	−79.2891			−0.505026			−0.252513	−	0.967594i	$-0.581257\pi$
$157$	−79.2891			−0.505026			−0.252513	+	0.967594i	$0.581257\pi$
$158$			173.222i			1.09634i
$159$	−247.771	−	144.428i	−1.55831	−	0.908351i
$160$	−12.6491			−0.0790569
$161$			60.3000i			0.374534i
$162$	−98.2379	−	58.9178i	−0.606407	−	0.363690i
$163$	−72.9838			−0.447753			−0.223877	−	0.974617i	$-0.571871\pi$
$163$	−72.9838			−0.447753			−0.223877	+	0.974617i	$0.571871\pi$
$164$		−	57.3701i		−	0.349817i
$165$	49.5694	−	85.0381i	0.300421	−	0.515382i
$166$	−96.5586			−0.581678
$167$			113.145i			0.677512i	0.940874	+	0.338756i	$0.110006\pi$
$167$			113.145i			0.677512i	−0.940874	+	0.338756i	$0.889994\pi$
$168$	−19.3954	−	11.3057i	−0.115449	−	0.0672960i
$169$	196.239			1.16118
$170$			94.2078i			0.554164i
$171$	−65.2998	−	115.307i	−0.381870	−	0.674309i
$172$	80.9604			0.470700
$173$			115.843i			0.669611i	0.942287	+	0.334806i	$0.108671\pi$
$173$			115.843i			0.669611i	−0.942287	+	0.334806i	$0.891329\pi$
$174$	110.231	−	189.105i	0.633512	−	1.08681i
$175$	13.2288			0.0755929
$176$			58.6927i			0.333481i
$177$	28.8608	+	16.8232i	0.163055	+	0.0950463i
$178$	112.319			0.631004
$179$			76.5353i			0.427572i	0.976881	+	0.213786i	$0.0685794\pi$
$179$			76.5353i			0.427572i	−0.976881	+	0.213786i	$0.931421\pi$
$180$	−35.0230	+	19.8340i	−0.194572	+	0.110189i
$181$	38.3458			0.211855			0.105928	−	0.994374i	$-0.466219\pi$
$181$	38.3458			0.211855			0.105928	+	0.994374i	$0.466219\pi$
$182$			71.5076i			0.392899i
$183$	157.320	−	269.889i	0.859674	−	1.47480i
$184$	−64.4634			−0.350344
$185$		−	65.3114i		−	0.353035i
$186$	141.843	+	82.6815i	0.762597	+	0.444524i
$187$	437.131			2.33760
$188$		−	21.1802i		−	0.112660i
$189$	−71.4297	−	0.891165i	−0.377935	−	0.00471516i
$190$	−46.5604			−0.245055
$191$		−	0.0103646i		−	5.42648e-5i	−1.00000		2.71324e-5i	$-0.999991\pi$
$191$		−	0.0103646i		−	5.42648e-5i	1.00000		2.71324e-5i	$-8.63652e-6\pi$
$192$	12.0863	−	20.7345i	0.0629496	−	0.107992i
$193$	14.2760			0.0739689			0.0369844	−	0.999316i	$-0.488225\pi$
$193$	14.2760			0.0739689			0.0369844	+	0.999316i	$0.488225\pi$
$194$		−	39.8878i		−	0.205607i
$195$	110.759	+	64.5621i	0.567993	+	0.331088i
$196$	−14.0000			−0.0714286
$197$			123.543i			0.627120i	0.949568	+	0.313560i	$0.101522\pi$
$197$			123.543i			0.627120i	−0.949568	+	0.313560i	$0.898478\pi$
$198$	92.0312	+	162.509i	0.464804	+	0.820753i
$199$	−187.525			−0.942335			−0.471167	−	0.882044i	$-0.656167\pi$
$199$	−187.525			−0.942335			−0.471167	+	0.882044i	$0.656167\pi$
$200$			14.1421i			0.0707107i
$201$	−68.3747	+	117.299i	−0.340173	+	0.583578i
$202$	−15.0995			−0.0747498
$203$		−	136.500i		−	0.672416i
$204$	−154.426	−	90.0164i	−0.756992	−	0.441257i
$205$	−64.1417			−0.312886
$206$			48.2307i			0.234129i
$207$	−178.487	+	101.080i	−0.862256	+	0.488307i
$208$	−76.4449			−0.367523
$209$			216.043i			1.03370i
$210$	−12.6402	+	21.6847i	−0.0601914	+	0.103260i
$211$	−280.253			−1.32821			−0.664106	−	0.747638i	$-0.731188\pi$
$211$	−280.253			−1.32821			−0.664106	+	0.747638i	$0.731188\pi$
$212$		−	191.195i		−	0.901863i
$213$	−243.103	−	141.707i	−1.14133	−	0.665290i
$214$	−21.8267			−0.101994
$215$		−	90.5165i		−	0.421007i
$216$	0.952696	−	76.3616i	0.00441063	−	0.353526i
$217$	102.385			0.471822
$218$		−	44.9004i		−	0.205965i
$219$	94.8990	−	162.803i	0.433329	−	0.743391i
$220$	65.6205			0.298275
$221$			569.345i			2.57622i
$222$	107.059	+	62.4056i	0.482248	+	0.281106i
$223$	−100.764			−0.451858			−0.225929	−	0.974144i	$-0.572542\pi$
$223$	−100.764			−0.451858			−0.225929	+	0.974144i	$0.572542\pi$
$224$		−	14.9666i		−	0.0668153i
$225$	22.1751	+	39.1569i	0.0985560	+	0.174031i
$226$	−37.0159			−0.163787
$227$			154.057i			0.678664i	0.940667	+	0.339332i	$0.110201\pi$
$227$			154.057i			0.678664i	−0.940667	+	0.339332i	$0.889799\pi$
$228$	44.4888	−	76.3221i	0.195126	−	0.334746i
$229$	395.080			1.72524			0.862621	−	0.505852i	$-0.168822\pi$
$229$	395.080			1.72524			0.862621	+	0.505852i	$0.168822\pi$
$230$			72.0722i			0.313358i
$231$	100.618	+	58.6513i	0.435578	+	0.253902i
$232$	145.925			0.628987
$233$			192.917i			0.827972i	0.910283	+	0.413986i	$0.135864\pi$
$233$			192.917i			0.827972i	−0.910283	+	0.413986i	$0.864136\pi$
$234$	−211.662	+	119.867i	−0.904537	+	0.512251i
$235$	−23.6801			−0.100767
$236$			22.2707i			0.0943675i
$237$	−185.051	+	317.462i	−0.780808	+	1.33950i
$238$	−111.468			−0.468354
$239$			312.840i			1.30896i	0.756081	+	0.654478i	$0.227112\pi$
$239$			312.840i			1.30896i	−0.756081	+	0.654478i	$0.772888\pi$
$240$	−23.1819	−	13.5129i	−0.0965913	−	0.0563039i
$241$	328.130			1.36153			0.680767	−	0.732500i	$-0.261647\pi$
$241$	328.130			1.36153			0.680767	+	0.732500i	$0.261647\pi$
$242$		−	133.364i		−	0.551089i
$243$	−117.098	−	212.925i	−0.481886	−	0.876234i
$244$	208.262			0.853533
$245$			15.6525i			0.0638877i
$246$	61.2879	−	105.142i	0.249138	−	0.427405i
$247$	−281.387			−1.13922
$248$			109.455i			0.441349i
$249$	−176.962	−	103.153i	−0.710691	−	0.414268i
$250$	15.8114			0.0632456
$251$		−	146.160i		−	0.582310i	−0.956676	−	0.291155i	$-0.905960\pi$
$251$		−	146.160i		−	0.582310i	0.956676	−	0.291155i	$-0.0940396\pi$
$252$	−23.4679	−	41.4398i	−0.0931267	−	0.164444i
$253$	334.420			1.32182
$254$			219.676i			0.864866i
$255$	−100.641	+	172.654i	−0.394672	+	0.677074i
$256$	16.0000			0.0625000
$257$		−	306.185i		−	1.19138i	−0.803214	−	0.595691i	$-0.796878\pi$
$257$		−	306.185i		−	1.19138i	0.803214	−	0.595691i	$-0.203122\pi$
$258$	148.375	+	86.4893i	0.575099	+	0.335230i
$259$	77.2775			0.298369
$260$			85.4680i			0.328723i
$261$	404.039	−	228.813i	1.54804	−	0.876678i
$262$	142.635			0.544410
$263$			158.182i			0.601452i	0.953711	+	0.300726i	$0.0972290\pi$
$263$			158.182i			0.601452i	−0.953711	+	0.300726i	$0.902771\pi$
$264$	−62.7009	+	107.566i	−0.237503	+	0.407446i
$265$	−213.762			−0.806651
$266$		−	55.0910i		−	0.207109i
$267$	205.845	+	119.989i	0.770956	+	0.449397i
$268$	−90.5151			−0.337743
$269$			158.158i			0.587948i	0.955813	+	0.293974i	$0.0949779\pi$
$269$			158.158i			0.587948i	−0.955813	+	0.293974i	$0.905022\pi$
$270$	−85.3749	−	1.06515i	−0.316203	−	0.00394499i
$271$	361.490			1.33391			0.666956	−	0.745097i	$-0.267597\pi$
$271$	361.490			1.33391			0.666956	+	0.745097i	$0.267597\pi$
$272$		−	119.165i		−	0.438105i
$273$	−76.3909	+	131.051i	−0.279820	+	0.480042i
$274$	166.413			0.607348
$275$		−	73.3659i		−	0.266785i
$276$	−118.141	−	68.8656i	−0.428049	−	0.249513i
$277$	−77.1087			−0.278371			−0.139185	−	0.990266i	$-0.544448\pi$
$277$	−77.1087			−0.278371			−0.139185	+	0.990266i	$0.544448\pi$
$278$		−	105.902i		−	0.380944i
$279$	171.627	+	303.059i	0.615149	+	1.08623i
$280$	−16.7332			−0.0597614
$281$		−	96.2437i		−	0.342504i	−0.985227	−	0.171252i	$-0.945219\pi$
$281$		−	96.2437i		−	0.342504i	0.985227	−	0.171252i	$-0.0547813\pi$
$282$	22.6266	−	38.8167i	0.0802361	−	0.137648i
$283$	210.868			0.745118			0.372559	−	0.928008i	$-0.378480\pi$
$283$	210.868			0.745118			0.372559	+	0.928008i	$0.378480\pi$
$284$		−	187.593i		−	0.660538i
$285$	−85.3307	−	49.7400i	−0.299406	−	0.174526i
$286$	396.577			1.38663
$287$		−	75.8935i		−	0.264437i
$288$	44.3010	−	25.0883i	0.153823	−	0.0871120i
$289$	−598.512			−2.07097
$290$		−	163.149i		−	0.562583i
$291$	42.6118	−	73.1020i	0.146432	−	0.251210i
$292$	125.628			0.430234
$293$		−	441.017i		−	1.50518i	−0.658491	−	0.752588i	$-0.728805\pi$
$293$		−	441.017i		−	1.50518i	0.658491	−	0.752588i	$-0.271195\pi$
$294$	−25.6577	−	14.9561i	−0.0872710	−	0.0508710i
$295$	24.8994			0.0844048
$296$			82.6131i			0.279098i
$297$	−4.94235	+	396.145i	−0.0166409	+	1.33382i
$298$	211.544			0.709879
$299$			435.569i			1.45675i
$300$	−15.1079	+	25.9182i	−0.0503597	+	0.0863939i
$301$	107.101			0.355816
$302$			286.529i			0.948773i
$303$	−27.6726	−	16.1306i	−0.0913288	−	0.0532363i
$304$	58.8947			0.193733
$305$		−	232.844i		−	0.763423i
$306$	−186.852	−	329.944i	−0.610627	−	1.07825i
$307$	253.872			0.826944			0.413472	−	0.910517i	$-0.364316\pi$
$307$	253.872			0.826944			0.413472	+	0.910517i	$0.364316\pi$
$308$			77.6432i			0.252088i
$309$	−51.5244	+	88.3919i	−0.166745	+	0.286058i
$310$	122.374			0.394755
$311$			402.715i			1.29490i	0.762106	+	0.647452i	$0.224165\pi$
$311$			402.715i			1.29490i	−0.762106	+	0.647452i	$0.775835\pi$
$312$	−140.100	−	81.6654i	−0.449038	−	0.261748i
$313$	58.4446			0.186724			0.0933620	−	0.995632i	$-0.470239\pi$
$313$	58.4446			0.186724			0.0933620	+	0.995632i	$0.470239\pi$
$314$		−	112.132i		−	0.357107i
$315$	−46.3311	+	26.2379i	−0.147083	+	0.0832950i
$316$	−244.973			−0.775231
$317$		−	181.889i		−	0.573783i	−0.957963	−	0.286891i	$-0.907378\pi$
$317$		−	181.889i		−	0.573783i	0.957963	−	0.286891i	$-0.0926219\pi$
$318$	204.252	−	350.401i	0.642301	−	1.10189i
$319$	−757.023			−2.37311
$320$		−	17.8885i		−	0.0559017i
$321$	−40.0015	−	23.3172i	−0.124615	−	0.0726393i
$322$	−85.2770			−0.264835
$323$		−	438.635i		−	1.35800i
$324$	83.3224	−	138.929i	0.257168	−	0.428795i
$325$	95.5561			0.294019
$326$		−	103.215i		−	0.316609i
$327$	47.9666	−	82.2885i	0.146687	−	0.251647i
$328$	81.1335			0.247358
$329$		−	28.0187i		−	0.0851633i
$330$	120.262	+	70.1017i	0.364430	+	0.212429i
$331$	359.994			1.08760			0.543798	−	0.839216i	$-0.316986\pi$
$331$	359.994			1.08760			0.543798	+	0.839216i	$0.316986\pi$
$332$		−	136.554i		−	0.411309i
$333$	129.539	+	228.740i	0.389005	+	0.686908i
$334$	−160.010			−0.479073
$335$			101.199i			0.302086i
$336$	15.9887	−	27.4292i	0.0475854	−	0.0816345i
$337$	−637.901			−1.89288			−0.946441	−	0.322878i	$-0.895350\pi$
$337$	−637.901			−1.89288			−0.946441	+	0.322878i	$0.895350\pi$
$338$			277.524i			0.821076i
$339$	−67.8388	−	39.5438i	−0.200114	−	0.116648i
$340$	−133.230			−0.391853
$341$		−	567.823i		−	1.66517i
$342$	163.068	−	92.3479i	0.476808	−	0.270023i
$343$	−18.5203			−0.0539949
$344$			114.495i			0.332835i
$345$	−76.9941	+	132.086i	−0.223171	+	0.382858i
$346$	−163.826			−0.473487
$347$		−	131.343i		−	0.378509i	−0.981928	−	0.189255i	$-0.939393\pi$
$347$		−	131.343i		−	0.378509i	0.981928	−	0.189255i	$-0.0606072\pi$
$348$	267.436	+	155.890i	0.768493	+	0.447961i
$349$	−462.012			−1.32382			−0.661908	−	0.749585i	$-0.730253\pi$
$349$	−462.012			−1.32382			−0.661908	+	0.749585i	$0.730253\pi$
$350$			18.7083i			0.0534522i
$351$	−515.963	−	6.43721i	−1.46998	−	0.0183396i
$352$	−83.0041			−0.235807
$353$		−	43.9668i		−	0.124552i	−0.998059	−	0.0622759i	$-0.980164\pi$
$353$		−	43.9668i		−	0.124552i	0.998059	−	0.0622759i	$-0.0198359\pi$
$354$	−23.7916	+	40.8153i	−0.0672079	+	0.115298i
$355$	−209.735			−0.590803
$356$			158.843i			0.446187i
$357$	−204.287	−	119.080i	−0.572232	−	0.333559i
$358$	−108.237			−0.302339
$359$		−	106.165i		−	0.295724i	−0.989008	−	0.147862i	$-0.952761\pi$
$359$		−	106.165i		−	0.295724i	0.989008	−	0.147862i	$-0.0472392\pi$
$360$	−28.0495	−	49.5300i	−0.0779154	−	0.137583i
$361$	−144.213			−0.399483
$362$			54.2291i			0.149804i
$363$	142.471	−	244.414i	0.392482	−	0.673317i
$364$	−101.127			−0.277822
$365$		−	140.457i		−	0.384813i
$366$	381.680	+	222.484i	1.04284	+	0.607881i
$367$	−181.497			−0.494543			−0.247272	−	0.968946i	$-0.579534\pi$
$367$	−181.497			−0.494543			−0.247272	+	0.968946i	$0.579534\pi$
$368$		−	91.1650i		−	0.247731i
$369$	224.644	−	127.219i	0.608790	−	0.344766i
$370$	92.3643			0.249633
$371$		−	252.927i		−	0.681744i
$372$	−116.929	+	200.596i	−0.314326	+	0.539238i
$373$	−12.3681			−0.0331585			−0.0165792	−	0.999863i	$-0.505278\pi$
$373$	−12.3681			−0.0331585			−0.0165792	+	0.999863i	$0.505278\pi$
$374$			618.196i			1.65293i
$375$	28.9774	+	16.8912i	0.0772730	+	0.0450431i
$376$	29.9533			0.0796630
$377$		−	985.992i		−	2.61536i
$378$	1.26030	−	101.017i	0.00333412	−	0.267240i
$379$	−423.772			−1.11813			−0.559067	−	0.829123i	$-0.688840\pi$
$379$	−423.772			−1.11813			−0.559067	+	0.829123i	$0.688840\pi$
$380$		−	65.8463i		−	0.173280i
$381$	−234.678	+	402.598i	−0.615952	+	1.05669i
$382$	0.0146577			3.83710e−5
$383$			485.717i			1.26819i	0.773255	+	0.634096i	$0.218627\pi$
$383$			485.717i			1.26819i	−0.773255	+	0.634096i	$0.781373\pi$
$384$	29.3231	+	17.0926i	0.0763621	+	0.0445121i
$385$	86.8077			0.225475
$386$			20.1893i			0.0523039i
$387$	179.531	+	317.016i	0.463903	+	0.819163i
$388$	56.4099			0.145386
$389$			205.829i			0.529123i	0.964369	+	0.264562i	$0.0852273\pi$
$389$			205.829i			0.529123i	−0.964369	+	0.264562i	$0.914773\pi$
$390$	−91.3046	+	156.636i	−0.234114	+	0.401632i
$391$	−678.977			−1.73651
$392$		−	19.7990i		−	0.0505076i
$393$	261.407	+	152.376i	0.665157	+	0.387726i
$394$	−174.716			−0.443441
$395$			273.888i			0.693387i
$396$	−229.823	+	130.152i	−0.580360	+	0.328666i
$397$	−266.721			−0.671842			−0.335921	−	0.941890i	$-0.609048\pi$
$397$	−266.721			−0.671842			−0.335921	+	0.941890i	$0.609048\pi$
$398$		−	265.200i		−	0.666331i
$399$	58.8532	−	100.965i	0.147502	−	0.253044i
$400$	−20.0000			−0.0500000
$401$		−	251.023i		−	0.625991i	−0.949755	−	0.312996i	$-0.898667\pi$
$401$		−	251.023i		−	0.625991i	0.949755	−	0.312996i	$-0.101333\pi$
$402$	−165.886	−	96.6964i	−0.412652	−	0.240538i
$403$	739.567			1.83515
$404$		−	21.3538i		−	0.0528561i
$405$	−155.328	−	93.1572i	−0.383525	−	0.230018i
$406$	193.041			0.475470
$407$		−	428.576i		−	1.05301i
$408$	127.302	−	218.392i	0.312016	−	0.535274i
$409$	588.064			1.43781			0.718905	−	0.695109i	$-0.244644\pi$
$409$	588.064			1.43781			0.718905	+	0.695109i	$0.244644\pi$
$410$		−	90.7100i		−	0.221244i
$411$	304.984	+	177.778i	0.742054	+	0.432550i
$412$	−68.2084			−0.165554
$413$			29.4614i			0.0713351i
$414$	−142.948	−	252.419i	−0.345285	−	0.609707i
$415$	−152.673			−0.367886
$416$		−	108.109i		−	0.259878i
$417$	113.135	−	194.086i	0.271306	−	0.465435i
$418$	−305.531			−0.730936
$419$			21.3662i			0.0509934i	0.999675	+	0.0254967i	$0.00811673\pi$
$419$			21.3662i			0.0509934i	−0.999675	+	0.0254967i	$0.991883\pi$
$420$	−30.6668	−	17.8759i	−0.0730161	−	0.0425617i
$421$	29.7516			0.0706688			0.0353344	−	0.999376i	$-0.488750\pi$
$421$	29.7516			0.0706688			0.0353344	+	0.999376i	$0.488750\pi$
$422$		−	396.337i		−	0.939188i
$423$	82.9350	−	46.9672i	0.196064	−	0.111034i
$424$	270.390			0.637713
$425$			148.956i			0.350484i
$426$	200.404	−	343.800i	0.470431	−	0.807041i
$427$	275.505			0.645210
$428$		−	30.8676i		−	0.0721205i
$429$	726.803	+	423.660i	1.69418	+	0.987552i
$430$	128.010			0.297697
$431$		−	44.2977i		−	0.102779i	−0.998679	−	0.0513894i	$-0.983635\pi$
$431$		−	44.2977i		−	0.102779i	0.998679	−	0.0513894i	$-0.0163650\pi$
$432$	107.992	+	1.34732i	0.249981	+	0.00311879i
$433$	−742.259			−1.71422			−0.857112	−	0.515131i	$-0.827743\pi$
$433$	−742.259			−1.71422			−0.857112	+	0.515131i	$0.827743\pi$
$434$			144.795i			0.333629i
$435$	174.291	−	299.002i	0.400668	−	0.687361i
$436$	63.4987			0.145639
$437$		−	335.571i		−	0.767897i
$438$	230.238	+	134.208i	0.525657	+	0.306410i
$439$	−339.668			−0.773732			−0.386866	−	0.922136i	$-0.626442\pi$
$439$	−339.668			−0.773732			−0.386866	+	0.922136i	$0.626442\pi$
$440$			92.8013i			0.210912i
$441$	−31.0451	−	54.8197i	−0.0703972	−	0.124308i
$442$	−805.175			−1.82166
$443$		−	7.56065i		−	0.0170669i	−0.999964	−	0.00853347i	$-0.997284\pi$
$443$		−	7.56065i		−	0.0170669i	0.999964	−	0.00853347i	$-0.00271632\pi$
$444$	−88.2548	+	151.404i	−0.198772	+	0.341001i
$445$	177.591			0.399082
$446$		−	142.502i		−	0.319512i
$447$	387.695	+	225.990i	0.867326	+	0.505571i
$448$	21.1660			0.0472456
$449$			480.937i			1.07113i	0.844494	+	0.535564i	$0.179901\pi$
$449$			480.937i			1.07113i	−0.844494	+	0.535564i	$0.820099\pi$
$450$	−55.3763	+	31.3603i	−0.123058	+	0.0696896i
$451$	−420.901			−0.933261
$452$		−	52.3484i		−	0.115815i
$453$	−306.097	+	525.120i	−0.675710	+	1.15921i
$454$	−217.869			−0.479888
$455$			113.064i			0.248491i
$456$	107.936	+	62.9167i	0.236701	+	0.137975i
$457$	593.531			1.29876			0.649378	−	0.760466i	$-0.275030\pi$
$457$	593.531			1.29876			0.649378	+	0.760466i	$0.275030\pi$
$458$			558.728i			1.21993i
$459$	10.0345	−	804.298i	0.0218617	−	1.75228i
$460$	−101.926			−0.221577
$461$			211.732i			0.459289i	0.973275	+	0.229645i	$0.0737564\pi$
$461$			211.732i			0.459289i	−0.973275	+	0.229645i	$0.926244\pi$
$462$	−82.9455	+	142.296i	−0.179536	+	0.308000i
$463$	618.360			1.33555			0.667776	−	0.744363i	$-0.267247\pi$
$463$	618.360			1.33555			0.667776	+	0.744363i	$0.267247\pi$
$464$			206.369i			0.444761i
$465$	224.274	+	130.731i	0.482309	+	0.281142i
$466$	−272.827			−0.585465
$467$			365.286i			0.782197i	0.920349	+	0.391099i	$0.127905\pi$
$467$			365.286i			0.782197i	−0.920349	+	0.391099i	$0.872095\pi$
$468$	−169.517	−	299.335i	−0.362217	−	0.639604i
$469$	−119.740			−0.255310
$470$		−	33.4888i		−	0.0712527i
$471$	119.789	−	205.503i	0.254330	−	0.436311i
$472$	−31.4956			−0.0667279
$473$		−	593.974i		−	1.25576i
$474$	−448.959	−	261.702i	−0.947172	−	0.552114i
$475$	−73.6184			−0.154986
$476$		−	157.640i		−	0.331176i
$477$	748.661	−	423.977i	1.56952	−	0.888840i
$478$	−442.423			−0.925571
$479$		−	167.464i		−	0.349611i	−0.984603	−	0.174805i	$-0.944070\pi$
$479$		−	167.464i		−	0.349611i	0.984603	−	0.174805i	$-0.0559296\pi$
$480$	19.1102	−	32.7842i	0.0398128	−	0.0683003i
$481$	558.203			1.16051
$482$			464.046i			0.962750i
$483$	−156.286	−	91.1006i	−0.323574	−	0.188614i
$484$	188.605			0.389679
$485$		−	63.0682i		−	0.130037i
$486$	301.121	−	165.602i	0.619591	−	0.340745i
$487$	−239.295			−0.491366			−0.245683	−	0.969350i	$-0.579012\pi$
$487$	−239.295			−0.491366			−0.245683	+	0.969350i	$0.579012\pi$
$488$			294.527i			0.603539i
$489$	110.263	−	189.161i	0.225487	−	0.386831i
$490$	−22.1359			−0.0451754
$491$		−	255.880i		−	0.521140i	−0.965455	−	0.260570i	$-0.916090\pi$
$491$		−	255.880i		−	0.521140i	0.965455	−	0.260570i	$-0.0839105\pi$
$492$	148.693	+	86.6742i	0.302221	+	0.176167i
$493$	1536.99			3.11763
$494$		−	397.942i		−	0.805551i
$495$	145.514	+	256.950i	0.293968	+	0.519090i
$496$	−154.792			−0.312081
$497$		−	248.162i		−	0.499320i
$498$	145.880	−	250.262i	0.292931	−	0.502534i
$499$	−78.1567			−0.156627			−0.0783133	−	0.996929i	$-0.524953\pi$
$499$	−78.1567			−0.156627			−0.0783133	+	0.996929i	$0.524953\pi$
$500$			22.3607i			0.0447214i
$501$	−293.250	−	170.938i	−0.585329	−	0.341193i
$502$	206.701			0.411755
$503$			756.325i			1.50363i	0.659375	+	0.751814i	$0.270821\pi$
$503$			756.325i			1.50363i	−0.659375	+	0.751814i	$0.729179\pi$
$504$	58.6047	−	33.1887i	0.116279	−	0.0658505i
$505$	−23.8743			−0.0472759
$506$			472.941i			0.934667i
$507$	−296.476	+	508.615i	−0.584765	+	1.00319i
$508$	−310.669			−0.611553
$509$		−	797.969i		−	1.56772i	−0.620938	−	0.783859i	$-0.713248\pi$
$509$		−	797.969i		−	1.56772i	0.620938	−	0.783859i	$-0.286752\pi$
$510$	−244.169	−	142.328i	−0.478763	−	0.279075i
$511$	166.191			0.325226
$512$			22.6274i			0.0441942i
$513$	397.508	+	4.95936i	0.774870	+	0.00966737i
$514$	433.011			0.842434
$515$			76.2594i			0.148076i
$516$	−122.314	+	209.835i	−0.237043	+	0.406656i
$517$	−155.390			−0.300561
$518$			109.287i			0.210979i
$519$	−300.243	−	175.014i	−0.578503	−	0.337214i
$520$	−120.870			−0.232442
$521$		−	22.5301i		−	0.0432440i	−0.999766	−	0.0216220i	$-0.993117\pi$
$521$		−	22.5301i		−	0.0432440i	0.999766	−	0.0216220i	$-0.00688303\pi$
$522$	323.590	+	571.398i	0.619905	+	1.09463i
$523$	250.580			0.479121			0.239560	−	0.970881i	$-0.422997\pi$
$523$	250.580			0.479121			0.239560	+	0.970881i	$0.422997\pi$
$524$			201.717i			0.384956i
$525$	−19.9859	+	34.2865i	−0.0380684	+	0.0653076i
$526$	−223.703			−0.425291
$527$			1152.86i			2.18759i
$528$	−152.121	−	88.6724i	−0.288107	−	0.167940i
$529$	9.55921			0.0180703
$530$		−	302.306i		−	0.570388i
$531$	−87.2053	+	49.3856i	−0.164228	+	0.0930048i
$532$	77.9104			0.146448
$533$		−	548.206i		−	1.02853i
$534$	−169.690	+	291.109i	−0.317772	+	0.545149i
$535$	−34.5110			−0.0645065
$536$		−	128.008i		−	0.238820i
$537$	−198.365	−	115.629i	−0.369396	−	0.215324i
$538$	−223.669			−0.415742
$539$			102.712i			0.190561i
$540$	1.50634	−	120.738i	0.00278953	−	0.223589i
$541$	−438.380			−0.810314			−0.405157	−	0.914247i	$-0.632783\pi$
$541$	−438.380			−0.810314			−0.405157	+	0.914247i	$0.632783\pi$
$542$			511.224i			0.943218i
$543$	−57.9324	+	99.3851i	−0.106690	+	0.183030i
$544$	168.524			0.309787
$545$		−	70.9937i		−	0.130264i
$546$	−185.335	−	108.033i	−0.339441	−	0.197863i
$547$	−212.261			−0.388045			−0.194023	−	0.980997i	$-0.562154\pi$
$547$	−212.261			−0.388045			−0.194023	+	0.980997i	$0.562154\pi$
$548$			235.344i			0.429460i
$549$	461.823	+	815.490i	0.841208	+	1.48541i
$550$	103.755			0.188646
$551$			759.628i			1.37864i
$552$	97.3907	−	167.077i	0.176432	−	0.302676i
$553$	−324.069			−0.586019
$554$		−	109.048i		−	0.196838i
$555$	169.275	+	98.6719i	0.305000	+	0.177787i
$556$	149.769			0.269368
$557$			303.846i			0.545504i	0.962084	+	0.272752i	$0.0879338\pi$
$557$			303.846i			0.545504i	−0.962084	+	0.272752i	$0.912066\pi$
$558$	−428.591	+	242.717i	−0.768083	+	0.434976i
$559$	773.626			1.38395
$560$		−	23.6643i		−	0.0422577i
$561$	−660.413	+	1132.96i	−1.17721	+	2.01954i
$562$	136.109			0.242187
$563$			59.7131i			0.106062i	0.998593	+	0.0530312i	$0.0168883\pi$
$563$			59.7131i			0.106062i	−0.998593	+	0.0530312i	$0.983112\pi$
$564$	54.8951	+	31.9988i	0.0973317	+	0.0567355i
$565$	−58.5273			−0.103588
$566$			298.213i			0.526878i
$567$	110.225	−	183.786i	0.194401	−	0.324138i
$568$	265.296			0.467071
$569$			125.358i			0.220313i	0.993914	+	0.110157i	$0.0351352\pi$
$569$			125.358i			0.220313i	−0.993914	+	0.110157i	$0.964865\pi$
$570$	70.3430	−	120.676i	0.123409	−	0.211712i
$571$	865.616			1.51597			0.757983	−	0.652275i	$-0.226185\pi$
$571$	865.616			1.51597			0.757983	+	0.652275i	$0.226185\pi$
$572$			560.845i			0.980498i
$573$	0.0268631	+	0.0156587i	4.68815e−5	+	2.73276e-5i
$574$	107.330			0.186985
$575$			113.956i			0.198185i
$576$	35.4802	+	62.6511i	0.0615975	+	0.108769i
$577$	176.822			0.306451			0.153225	−	0.988191i	$-0.451034\pi$
$577$	176.822			0.306451			0.153225	+	0.988191i	$0.451034\pi$
$578$		−	846.423i		−	1.46440i
$579$	−21.5680	+	37.0007i	−0.0372505	+	0.0639046i
$580$	230.728			0.397807
$581$		−	180.645i		−	0.310920i
$582$	103.382	+	60.2621i	0.177632	+	0.103543i
$583$	−1402.72			−2.40604
$584$			177.665i			0.304221i
$585$	−334.666	+	189.526i	−0.572079	+	0.323976i
$586$	623.692			1.06432
$587$		−	330.200i		−	0.562521i	−0.959631	−	0.281260i	$-0.909248\pi$
$587$		−	330.200i		−	0.562521i	0.959631	−	0.281260i	$-0.0907525\pi$
$588$	21.1511	−	36.2854i	0.0359712	−	0.0617099i
$589$	−569.778			−0.967364
$590$			35.2131i			0.0596832i
$591$	−320.200	−	186.647i	−0.541793	−	0.315816i
$592$	−116.833			−0.197352
$593$			996.327i			1.68015i	0.542473	+	0.840073i	$0.317488\pi$
$593$			996.327i			1.68015i	−0.542473	+	0.840073i	$0.682512\pi$
$594$	−560.234	−	6.98954i	−0.943154	−	0.0117669i
$595$	−176.247			−0.296213
$596$			299.168i			0.501960i
$597$	283.311	−	486.029i	0.474557	−	0.814119i
$598$	−615.987			−1.03008
$599$		−	416.236i		−	0.694885i	−0.937701	−	0.347443i	$-0.887050\pi$
$599$		−	416.236i		−	0.694885i	0.937701	−	0.347443i	$-0.112950\pi$
$600$	−36.6538	−	21.3658i	−0.0610897	−	0.0356097i
$601$	1141.63			1.89955			0.949777	−	0.312929i	$-0.101310\pi$
$601$	1141.63			1.89955			0.949777	+	0.312929i	$0.101310\pi$
$602$			151.463i			0.251600i
$603$	−200.718	−	354.429i	−0.332866	−	0.587776i
$604$	−405.214			−0.670884
$605$		−	210.866i		−	0.348539i
$606$	22.8121	−	39.1350i	0.0376438	−	0.0645792i
$607$	−664.913			−1.09541			−0.547704	−	0.836672i	$-0.684498\pi$
$607$	−664.913			−1.09541			−0.547704	+	0.836672i	$0.684498\pi$
$608$			83.2897i			0.136990i
$609$	353.784	+	206.224i	0.580926	+	0.338627i
$610$	329.291			0.539822
$611$		−	202.389i		−	0.331243i
$612$	466.612	−	264.249i	0.762437	−	0.431779i
$613$	−588.435			−0.959927			−0.479963	−	0.877289i	$-0.659350\pi$
$613$	−588.435			−0.959927			−0.479963	+	0.877289i	$0.659350\pi$
$614$			359.029i			0.584738i
$615$	96.9047	−	166.243i	0.157569	−	0.270315i
$616$	−109.804			−0.178253
$617$		−	631.416i		−	1.02336i	−0.859175	−	0.511682i	$-0.829022\pi$
$617$		−	631.416i		−	1.02336i	0.859175	−	0.511682i	$-0.170978\pi$
$618$	−125.005	−	72.8664i	−0.202273	−	0.117907i
$619$	−335.858			−0.542582			−0.271291	−	0.962497i	$-0.587451\pi$
$619$	−335.858			−0.542582			−0.271291	+	0.962497i	$0.587451\pi$
$620$			173.063i			0.279134i
$621$	7.67675	−	615.316i	0.0123619	−	0.990847i
$622$	−569.525			−0.915635
$623$			210.129i			0.337286i
$624$	115.492	−	198.131i	0.185084	−	0.317518i
$625$	25.0000			0.0400000
$626$			82.6532i			0.132034i
$627$	−559.944	−	326.396i	−0.893053	−	0.520568i
$628$	158.578			0.252513
$629$			870.144i			1.38338i
$630$	−37.1060	−	65.5221i	−0.0588985	−	0.104003i
$631$	−641.185			−1.01614			−0.508070	−	0.861316i	$-0.669641\pi$
$631$	−641.185			−1.01614			−0.508070	+	0.861316i	$0.669641\pi$
$632$		−	346.444i		−	0.548171i
$633$	423.403	−	726.364i	0.668884	−	1.14749i
$634$	257.230			0.405726
$635$			347.338i			0.546989i
$636$	495.542	+	288.856i	0.779154	+	0.454175i
$637$	−133.779			−0.210013
$638$		−	1070.59i		−	1.67804i
$639$	734.556	−	415.989i	1.14954	−	0.651000i
$640$	25.2982			0.0395285
$641$			358.234i			0.558867i	0.960165	+	0.279433i	$0.0901466\pi$
$641$			358.234i			0.558867i	−0.960165	+	0.279433i	$0.909853\pi$
$642$	32.9755	−	56.5707i	0.0513638	−	0.0881164i
$643$	−1218.12			−1.89443			−0.947213	−	0.320606i	$-0.896114\pi$
$643$	−1218.12			−1.89443			−0.947213	+	0.320606i	$0.896114\pi$
$644$		−	120.600i		−	0.187267i
$645$	234.602	+	136.752i	0.363724	+	0.212018i
$646$	620.324			0.960253
$647$			706.621i			1.09215i	0.837737	+	0.546075i	$0.183879\pi$
$647$			706.621i			1.09215i	−0.837737	+	0.546075i	$0.816121\pi$
$648$	196.476	+	117.836i	0.303204	+	0.181845i
$649$	163.391			0.251758
$650$			135.137i			0.207903i
$651$	−154.683	+	265.364i	−0.237608	+	0.407625i
$652$	145.968			0.223877
$653$			647.469i			0.991531i	0.868457	+	0.495765i	$0.165112\pi$
$653$			647.469i			0.991531i	−0.868457	+	0.495765i	$0.834888\pi$
$654$	116.373	+	67.8351i	0.177941	+	0.103723i
$655$	225.526			0.344315
$656$			114.740i			0.174909i
$657$	278.582	+	491.922i	0.424021	+	0.748739i
$658$	39.6245			0.0602196
$659$		−	925.263i		−	1.40404i	−0.712157	−	0.702020i	$-0.752282\pi$
$659$		−	925.263i		−	1.40404i	0.712157	−	0.702020i	$-0.247718\pi$
$660$	−99.1388	+	170.076i	−0.150210	+	0.257691i
$661$	516.011			0.780652			0.390326	−	0.920677i	$-0.372362\pi$
$661$	516.011			0.780652			0.390326	+	0.920677i	$0.372362\pi$
$662$			509.109i			0.769047i
$663$	−1475.64	−	860.161i	−2.22570	−	1.29738i
$664$	193.117			0.290839
$665$		−	87.1065i		−	0.130987i
$666$	−323.488	+	183.195i	−0.485717	+	0.275068i
$667$	1175.85			1.76290
$668$		−	226.289i		−	0.338756i
$669$	152.234	−	261.163i	0.227555	−	0.390378i
$670$	−143.117			−0.213607
$671$		−	1527.93i		−	2.27710i
$672$	38.7908	+	22.6115i	0.0577243	+	0.0336480i
$673$	1260.47			1.87291			0.936457	−	0.350782i	$-0.114084\pi$
$673$	1260.47			1.87291			0.936457	+	0.350782i	$0.114084\pi$
$674$		−	902.128i		−	1.33847i
$675$	−134.989	−	1.68414i	−0.199984	−	0.00249503i
$676$	−392.478			−0.580588
$677$		−	364.477i		−	0.538370i	−0.963088	−	0.269185i	$-0.913246\pi$
$677$		−	364.477i		−	0.538370i	0.963088	−	0.269185i	$-0.0867543\pi$
$678$	55.9233	−	95.9385i	0.0824828	−	0.141502i
$679$	74.6232			0.109902
$680$		−	188.416i		−	0.277082i
$681$	−399.286	−	232.747i	−0.586324	−	0.341773i
$682$	803.024			1.17745
$683$			335.908i			0.491813i	0.969294	+	0.245906i	$0.0790856\pi$
$683$			335.908i			0.491813i	−0.969294	+	0.245906i	$0.920914\pi$
$684$	130.600	+	230.614i	0.190935	+	0.337154i
$685$	263.123			0.384121
$686$		−	26.1916i		−	0.0381802i
$687$	−596.884	+	1023.98i	−0.868826	+	1.49050i
$688$	−161.921			−0.235350
$689$		−	1826.98i		−	2.65165i
$690$	−186.798	−	108.886i	−0.270722	−	0.157806i
$691$	56.3269			0.0815150			0.0407575	−	0.999169i	$-0.487023\pi$
$691$	56.3269			0.0815150			0.0407575	+	0.999169i	$0.487023\pi$
$692$		−	231.686i		−	0.334806i
$693$	−304.027	+	172.175i	−0.438711	+	0.248448i
$694$	185.747			0.267647
$695$		−	167.446i		−	0.240930i
$696$	−220.462	+	378.211i	−0.316756	+	0.543407i
$697$	854.560			1.22605
$698$		−	653.383i		−	0.936079i
$699$	−500.007	−	291.458i	−0.715317	−	0.416964i
$700$	−26.4575			−0.0377964
$701$		−	795.844i		−	1.13530i	−0.823270	−	0.567649i	$-0.807853\pi$
$701$		−	795.844i		−	1.13530i	0.823270	−	0.567649i	$-0.192147\pi$
$702$	9.10359	−	729.682i	0.0129681	−	1.03943i
$703$	−430.051			−0.611737
$704$		−	117.385i		−	0.166741i
$705$	35.7758	−	61.3746i	0.0507458	−	0.0870561i
$706$	62.1784			0.0880714
$707$		−	28.2485i		−	0.0399554i
$708$	−57.7216	−	33.6464i	−0.0815277	−	0.0475232i
$709$	127.721			0.180142			0.0900712	−	0.995935i	$-0.471291\pi$
$709$	127.721			0.180142			0.0900712	+	0.995935i	$0.471291\pi$
$710$		−	296.610i		−	0.417761i
$711$	−543.230	−	959.238i	−0.764036	−	1.34914i
$712$	−224.637			−0.315502
$713$			881.977i			1.23699i
$714$	168.405	−	288.905i	0.235862	−	0.404629i
$715$	627.044			0.876984
$716$		−	153.071i		−	0.213786i
$717$	−810.825	−	472.637i	−1.13086	−	0.659186i
$718$	150.140			0.209108
$719$		−	652.748i		−	0.907855i	−0.891039	−	0.453927i	$-0.850023\pi$
$719$		−	652.748i		−	0.907855i	0.891039	−	0.453927i	$-0.149977\pi$
$720$	70.0460	−	39.6680i	0.0972862	−	0.0550945i
$721$	−90.2313			−0.125147
$722$		−	203.948i		−	0.282477i
$723$	−495.736	+	850.452i	−0.685665	+	1.17628i
$724$	−76.6915			−0.105928
$725$		−	257.962i		−	0.355809i
$726$	345.654	+	201.484i	0.476107	+	0.277527i
$727$	181.338			0.249433			0.124717	−	0.992192i	$-0.460198\pi$
$727$	181.338			0.249433			0.124717	+	0.992192i	$0.460198\pi$
$728$		−	143.015i		−	0.196450i
$729$	728.773	+	18.1873i	0.999689	+	0.0249483i
$730$	198.636			0.272104
$731$			1205.95i			1.64973i
$732$	−314.641	+	539.777i	−0.429837	+	0.737400i
$733$	−980.665			−1.33788			−0.668939	−	0.743317i	$-0.733251\pi$
$733$	−980.665			−1.33788			−0.668939	+	0.743317i	$0.733251\pi$
$734$		−	256.676i		−	0.349695i
$735$	−40.5683	−	23.6476i	−0.0551950	−	0.0321736i
$736$	128.927			0.175172
$737$			664.072i			0.901047i
$738$	179.914	+	317.694i	0.243786	+	0.430480i
$739$	115.426			0.156193			0.0780963	−	0.996946i	$-0.475116\pi$
$739$	115.426			0.156193			0.0780963	+	0.996946i	$0.475116\pi$
$740$			130.623i			0.176517i
$741$	425.118	−	729.305i	0.573708	−	0.984217i
$742$	357.693			0.482066
$743$		−	131.260i		−	0.176662i	−0.996091	−	0.0883311i	$-0.971847\pi$
$743$		−	131.260i		−	0.176662i	0.996091	−	0.0883311i	$-0.0281534\pi$
$744$	−283.686	−	165.363i	−0.381299	−	0.222262i
$745$	334.480			0.448967
$746$		−	17.4911i		−	0.0234466i
$747$	534.705	−	302.811i	0.715804	−	0.405369i
$748$	−874.261			−1.16880
$749$		−	40.8340i		−	0.0545180i
$750$	−23.8877	+	40.9802i	−0.0318503	+	0.0546403i
$751$	−1088.21			−1.44902			−0.724508	−	0.689266i	$-0.757933\pi$
$751$	−1088.21			−1.44902			−0.724508	+	0.689266i	$0.757933\pi$
$752$			42.3603i			0.0563302i
$753$	378.819	+	220.817i	0.503080	+	0.293250i
$754$	1394.40			1.84934
$755$			453.043i			0.600057i
$756$	142.859	+	1.78233i	0.188968	+	0.00235758i
$757$	−1115.02			−1.47295			−0.736473	−	0.676467i	$-0.763510\pi$
$757$	−1115.02			−1.47295			−0.736473	+	0.676467i	$0.763510\pi$
$758$		−	599.305i		−	0.790639i
$759$	−505.239	+	866.755i	−0.665664	+	1.14197i
$760$	93.1207			0.122527
$761$			632.008i			0.830497i	0.909708	+	0.415249i	$0.136305\pi$
$761$			632.008i			0.830497i	−0.909708	+	0.415249i	$0.863695\pi$
$762$	−569.360	−	331.885i	−0.747191	−	0.435544i
$763$	84.0009			0.110093
$764$			0.0207292i			2.71324e-5i
$765$	−295.439	−	521.688i	−0.386195	−	0.681945i
$766$	−686.908			−0.896746
$767$			212.810i			0.277458i
$768$	−24.1727	+	41.4691i	−0.0314748	+	0.0539962i
$769$	183.616			0.238773			0.119386	−	0.992848i	$-0.461907\pi$
$769$	183.616			0.238773			0.119386	+	0.992848i	$0.461907\pi$
$770$			122.765i			0.159435i
$771$	793.575	+	462.582i	1.02928	+	0.599976i
$772$	−28.5520			−0.0369844
$773$			239.771i			0.310182i	0.987900	+	0.155091i	$0.0495671\pi$
$773$			239.771i			0.310182i	−0.987900	+	0.155091i	$0.950433\pi$
$774$	−448.329	+	253.895i	−0.579236	+	0.328029i
$775$	193.490			0.249665
$776$			79.7756i			0.102804i
$777$	−116.750	+	200.289i	−0.150258	+	0.257772i
$778$	−291.086			−0.374147
$779$			422.349i			0.542168i
$780$	−221.517	−	129.124i	−0.283997	−	0.165544i
$781$	−1376.29			−1.76222
$782$		−	960.218i		−	1.22790i
$783$	−17.3778	+	1392.88i	−0.0221938	+	1.77891i
$784$	28.0000			0.0357143
$785$		−	177.296i		−	0.225854i
$786$	−215.492	+	369.685i	−0.274163	+	0.470337i
$787$	−430.055			−0.546449			−0.273224	−	0.961950i	$-0.588090\pi$
$787$	−430.055			−0.546449			−0.273224	+	0.961950i	$0.588090\pi$
$788$		−	247.085i		−	0.313560i
$789$	−409.978	−	238.980i	−0.519618	−	0.302889i
$790$	−387.336			−0.490299
$791$		−	69.2505i		−	0.0875480i
$792$	−184.062	−	325.018i	−0.232402	−	0.410377i
$793$	1990.07			2.50955
$794$		−	377.201i		−	0.475064i
$795$	322.950	−	554.033i	0.406227	−	0.696897i
$796$	375.049			0.471167
$797$			454.406i			0.570146i	0.958506	+	0.285073i	$0.0920178\pi$
$797$			454.406i			0.570146i	−0.958506	+	0.285073i	$0.907982\pi$
$798$	142.786	+	83.2309i	0.178929	+	0.104299i
$799$	315.491			0.394857
$800$		−	28.2843i		−	0.0353553i
$801$	−621.979	+	352.235i	−0.776503	+	0.439744i
$802$	354.999			0.442643
$803$		−	921.683i		−	1.14780i
$804$	136.749	−	234.598i	0.170086	−	0.291789i
$805$	−134.835			−0.167497
$806$			1045.91i			1.29765i
$807$	−409.916	−	238.944i	−0.507951	−	0.296089i
$808$	30.1989			0.0373749
$809$			1016.61i			1.25662i	0.777963	+	0.628310i	$0.216253\pi$
$809$			1016.61i			1.25662i	−0.777963	+	0.628310i	$0.783747\pi$
$810$	131.744	−	219.667i	0.162647	−	0.271193i
$811$	756.253			0.932494			0.466247	−	0.884654i	$-0.345606\pi$
$811$	756.253			0.932494			0.466247	+	0.884654i	$0.345606\pi$
$812$			273.001i			0.336208i
$813$	−546.136	+	936.916i	−0.671754	+	1.15242i
$814$	606.099			0.744593
$815$		−	163.197i		−	0.200241i
$816$	308.853	+	180.033i	0.378496	+	0.220628i
$817$	−596.018			−0.729520
$818$			831.648i			1.01668i
$819$	−224.250	−	395.983i	−0.273810	−	0.483495i
$820$	128.283			0.156443
$821$		−	1207.04i		−	1.47021i	−0.677955	−	0.735104i	$-0.737134\pi$
$821$		−	1207.04i		−	1.47021i	0.677955	−	0.735104i	$-0.262866\pi$
$822$	−251.416	+	431.313i	−0.305859	+	0.524712i
$823$	169.449			0.205891			0.102946	−	0.994687i	$-0.467173\pi$
$823$	169.449			0.205891			0.102946	+	0.994687i	$0.467173\pi$
$824$		−	96.4613i		−	0.117065i
$825$	190.151	+	110.841i	0.230486	+	0.134352i
$826$	−41.6647			−0.0504415
$827$			953.176i			1.15257i	0.817248	+	0.576285i	$0.195498\pi$
$827$			953.176i			1.15257i	−0.817248	+	0.576285i	$0.804502\pi$
$828$	356.974	−	202.159i	0.431128	−	0.244154i
$829$	−6.32036			−0.00762407			−0.00381204	−	0.999993i	$-0.501213\pi$
$829$	−6.32036			−0.00762407			−0.00381204	+	0.999993i	$0.501213\pi$
$830$		−	215.912i		−	0.260134i
$831$	116.495	−	199.852i	0.140187	−	0.240495i
$832$	152.890			0.183762
$833$		−	208.538i		−	0.250346i
$834$	274.480	+	159.996i	0.329112	+	0.191842i
$835$	−252.999			−0.302993
$836$		−	432.086i		−	0.516850i
$837$	−1044.77	−	13.0346i	−1.24823	−	0.0155730i
$838$	−30.2164			−0.0360578
$839$		−	1230.70i		−	1.46686i	−0.679764	−	0.733430i	$-0.737918\pi$
$839$		−	1230.70i		−	1.46686i	0.679764	−	0.733430i	$-0.262082\pi$
$840$	25.2804	−	43.3694i	0.0300957	−	0.0516302i
$841$	−1820.77			−2.16500
$842$			42.0751i			0.0499704i
$843$	249.446	+	145.404i	0.295903	+	0.172484i
$844$	560.506			0.664106
$845$			438.803i			0.519294i
$846$	66.4217	+	117.288i	0.0785127	+	0.138638i
$847$	249.500			0.294569
$848$			382.390i			0.450931i
$849$	−318.578	+	546.532i	−0.375239	+	0.643737i
$850$	−210.655			−0.247830
$851$			665.690i			0.782244i
$852$	486.206	+	283.414i	0.570664	+	0.332645i
$853$	759.822			0.890764			0.445382	−	0.895341i	$-0.353068\pi$
$853$	759.822			0.890764			0.445382	+	0.895341i	$0.353068\pi$
$854$			389.623i			0.456233i
$855$	257.834	−	146.015i	0.301560	−	0.170778i
$856$	43.6533			0.0509969
$857$		−	531.002i		−	0.619606i	−0.950801	−	0.309803i	$-0.899737\pi$
$857$		−	531.002i		−	0.619606i	0.950801	−	0.309803i	$-0.100263\pi$
$858$	−599.145	+	1027.86i	−0.698305	+	1.19797i
$859$	765.291			0.890910			0.445455	−	0.895304i	$-0.353042\pi$
$859$	765.291			0.890910			0.445455	+	0.895304i	$0.353042\pi$
$860$			181.033i			0.210504i
$861$	196.702	+	114.659i	0.228457	+	0.133170i
$862$	62.6464			0.0726756
$863$			1329.43i			1.54048i	0.637754	+	0.770240i	$0.279864\pi$
$863$			1329.43i			1.54048i	−0.637754	+	0.770240i	$0.720136\pi$
$864$	−1.90539	+	152.723i	−0.00220531	+	0.176763i
$865$	−259.032			−0.299459
$866$		−	1049.71i		−	1.21214i
$867$	904.226	−	1551.23i	1.04294	−	1.78919i
$868$	−204.771			−0.235911
$869$			1797.27i			2.06820i
$870$	422.853	+	246.484i	0.486038	+	0.283315i
$871$	−864.927			−0.993027
$872$			89.8007i			0.102982i
$873$	125.089	+	220.884i	0.143287	+	0.253017i
$874$	474.569			0.542985
$875$			29.5804i			0.0338062i
$876$	−189.798	+	325.605i	−0.216664	+	0.371696i
$877$	−919.329			−1.04827			−0.524133	−	0.851637i	$-0.675610\pi$
$877$	−919.329			−1.04827			−0.524133	+	0.851637i	$0.675610\pi$
$878$		−	480.364i		−	0.547111i
$879$	1143.03	+	666.284i	1.30038	+	0.758002i
$880$	−131.241			−0.149137
$881$		−	832.315i		−	0.944739i	−0.881401	−	0.472369i	$-0.843399\pi$
$881$		−	832.315i		−	0.944739i	0.881401	−	0.472369i	$-0.156601\pi$
$882$	77.5268	−	43.9045i	0.0878988	−	0.0497783i
$883$	1425.51			1.61439			0.807196	−	0.590284i	$-0.200984\pi$
$883$	1425.51			1.61439			0.807196	+	0.590284i	$0.200984\pi$
$884$		−	1138.69i		−	1.28811i
$885$	−37.6178	+	64.5347i	−0.0425060	+	0.0729206i
$886$	10.6924			0.0120681
$887$			641.162i			0.722843i	0.932402	+	0.361422i	$0.117709\pi$
$887$			641.162i			0.722843i	−0.932402	+	0.361422i	$0.882291\pi$
$888$	−214.118	−	124.811i	−0.241124	−	0.140553i
$889$	−410.976			−0.462290
$890$			251.152i			0.282193i
$891$	−1019.27	−	611.302i	−1.14396	−	0.686085i
$892$	201.529			0.225929
$893$			155.925i			0.174608i
$894$	−319.599	+	548.283i	−0.357493	+	0.613292i
$895$	−171.138			−0.191216
$896$			29.9333i			0.0334077i
$897$	−1128.91	−	658.053i	−1.25854	−	0.733615i
$898$	−680.147			−0.757402
$899$		−	1996.52i		−	2.22082i
$900$	−44.3502	−	78.3139i	−0.0492780	−	0.0870154i
$901$	2847.96			3.16088
$902$		−	595.243i		−	0.659915i
$903$	−161.807	+	277.585i	−0.179188	+	0.307403i
$904$	74.0319			0.0818937
$905$			85.7437i			0.0947444i
$906$	−742.632	−	432.886i	−0.819682	−	0.477799i
$907$	1569.63			1.73057			0.865287	−	0.501278i	$-0.167136\pi$
$907$	1569.63			1.73057			0.865287	+	0.501278i	$0.167136\pi$
$908$		−	308.113i		−	0.339332i
$909$	83.6151	−	47.3524i	0.0919858	−	0.0520928i
$910$	−159.896			−0.175710
$911$			1742.53i			1.91277i	0.292108	+	0.956385i	$0.405643\pi$
$911$			1742.53i			1.91277i	−0.292108	+	0.956385i	$0.594357\pi$
$912$	−88.9776	+	152.644i	−0.0975632	+	0.167373i
$913$	−1001.84			−1.09731
$914$			839.380i			0.918359i
$915$	603.489	+	351.779i	0.659551	+	0.384458i
$916$	−790.160			−0.862621
$917$			266.847i			0.291000i
$918$	1137.45	+	14.1909i	1.23905	+	0.0154585i
$919$	−944.373			−1.02761			−0.513805	−	0.857907i	$-0.671764\pi$
$919$	−944.373			−1.02761			−0.513805	+	0.857907i	$0.671764\pi$
$920$		−	144.144i		−	0.156679i
$921$	−383.547	+	657.989i	−0.416447	+	0.714429i
$922$	−299.435			−0.324767
$923$		−	1792.56i		−	1.94211i
$924$	−201.237	−	117.303i	−0.217789	−	0.126951i
$925$	146.041			0.157882
$926$			874.494i			0.944377i
$927$	−151.253	−	267.083i	−0.163164	−	0.288116i
$928$	−291.850			−0.314494
$929$			600.958i			0.646887i	0.946248	+	0.323443i	$0.104841\pi$
$929$			600.958i			0.646887i	−0.946248	+	0.323443i	$0.895159\pi$
$930$	−184.881	+	317.171i	−0.198797	+	0.341044i
$931$	103.066			0.110704
$932$		−	385.835i		−	0.413986i
$933$	−1043.76	−	608.418i	−1.11872	−	0.652110i
$934$	−516.593			−0.553097
$935$			977.454i			1.04541i
$936$	423.323	−	239.734i	0.452268	−	0.256126i
$937$	−19.4399			−0.0207470			−0.0103735	−	0.999946i	$-0.503302\pi$
$937$	−19.4399			−0.0207470			−0.0103735	+	0.999946i	$0.503302\pi$
$938$		−	169.338i		−	0.180531i
$939$	−88.2976	+	151.478i	−0.0940336	+	0.161318i
$940$	47.3603			0.0503833
$941$		−	709.230i		−	0.753698i	−0.926275	−	0.376849i	$-0.877008\pi$
$941$		−	709.230i		−	0.753698i	0.926275	−	0.376849i	$-0.122992\pi$
$942$	290.625	+	169.408i	0.308519	+	0.179838i
$943$	653.768			0.693285
$944$		−	44.5414i		−	0.0471837i
$945$	1.99271	−	159.722i	0.00210868	−	0.169018i
$946$	840.006			0.887955
$947$		−	228.266i		−	0.241041i	−0.992711	−	0.120521i	$-0.961544\pi$
$947$		−	228.266i		−	0.241041i	0.992711	−	0.120521i	$-0.0384564\pi$
$948$	370.103	−	634.925i	0.390404	−	0.669752i
$949$	1200.45			1.26497
$950$		−	104.112i		−	0.109592i
$951$	471.423	+	274.796i	0.495713	+	0.288955i
$952$	222.936			0.234177
$953$		−	830.703i		−	0.871672i	−0.900026	−	0.435836i	$-0.856453\pi$
$953$		−	830.703i		−	0.871672i	0.900026	−	0.435836i	$-0.143547\pi$
$954$	599.594	+	1058.77i	0.628505	+	1.10982i
$955$	0.0231759			2.42680e−5
$956$		−	625.681i		−	0.654478i
$957$	1143.70	−	1962.06i	1.19509	−	2.05022i
$958$	236.829			0.247212
$959$			311.331i			0.324641i
$960$	46.3638	+	27.0259i	0.0482956	+	0.0281519i
$961$	536.539			0.558313
$962$			789.419i			0.820602i
$963$	120.868	−	68.4491i	0.125512	−	0.0710791i
$964$	−656.260			−0.680767
$965$			31.9221i			0.0330799i
$966$	128.836	−	221.022i	0.133370	−	0.228802i
$967$	1120.26			1.15849			0.579246	−	0.815153i	$-0.303347\pi$
$967$	1120.26			1.15849			0.579246	+	0.815153i	$0.303347\pi$
$968$			266.727i			0.275544i
$969$	1136.86	+	662.686i	1.17323	+	0.683886i
$970$	89.1918			0.0919504
$971$			533.802i			0.549745i	0.961481	+	0.274872i	$0.0886356\pi$
$971$			533.802i			0.549745i	−0.961481	+	0.274872i	$0.911364\pi$
$972$	234.197	+	425.850i	0.240943	+	0.438117i
$973$	198.125			0.203623
$974$		−	338.414i		−	0.347448i
$975$	−144.365	+	247.664i	−0.148067	+	0.254014i
$976$	−416.524			−0.426767
$977$		−	1232.14i		−	1.26115i	−0.776129	−	0.630575i	$-0.782819\pi$
$977$		−	1232.14i		−	1.26115i	0.776129	−	0.630575i	$-0.217181\pi$
$978$	267.513	+	155.936i	0.273531	+	0.159444i
$979$	1165.36			1.19036
$980$		−	31.3050i		−	0.0319438i
$981$	140.809	+	248.641i	0.143536	+	0.253457i
$982$	361.868			0.368502
$983$			1098.64i			1.11764i	0.829289	+	0.558820i	$0.188746\pi$
$983$			1098.64i			1.11764i	−0.829289	+	0.558820i	$0.811254\pi$
$984$	−122.576	+	210.283i	−0.124569	+	0.213702i
$985$	−276.250			−0.280457
$986$			2173.64i			2.20450i
$987$	72.6194	+	42.3304i	0.0735759	+	0.0428880i
$988$	562.775			0.569610
$989$			922.595i			0.932856i
$990$	−363.382	+	205.788i	−0.367052	+	0.207867i
$991$	−1388.10			−1.40070			−0.700352	−	0.713798i	$-0.746973\pi$
$991$	−1388.10			−1.40070			−0.700352	+	0.713798i	$0.746973\pi$
$992$		−	218.909i		−	0.220675i
$993$	−543.876	+	933.039i	−0.547710	+	0.939617i
$994$	350.954			0.353073
$995$		−	419.318i		−	0.421425i
$996$	353.924	+	206.305i	0.355345	+	0.207134i
$997$	−818.089			−0.820551			−0.410275	−	0.911962i	$-0.634567\pi$
$997$	−818.089			−0.820551			−0.410275	+	0.911962i	$0.634567\pi$
$998$		−	110.530i		−	0.110752i
$999$	−788.558	−	9.83814i	−0.789348	−	0.00984799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.e.a.71.12	yes	16
3.2	odd	2	inner	210.3.e.a.71.4	✓	16
4.3	odd	2		1680.3.l.c.1121.9		16
5.2	odd	4		1050.3.c.c.449.16		32
5.3	odd	4		1050.3.c.c.449.17		32
5.4	even	2		1050.3.e.d.701.5		16
12.11	even	2		1680.3.l.c.1121.10		16
15.2	even	4		1050.3.c.c.449.18		32
15.8	even	4		1050.3.c.c.449.15		32
15.14	odd	2		1050.3.e.d.701.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.e.a.71.4	✓	16	3.2	odd	2	inner
210.3.e.a.71.12	yes	16	1.1	even	1	trivial
1050.3.c.c.449.15		32	15.8	even	4
1050.3.c.c.449.16		32	5.2	odd	4
1050.3.c.c.449.17		32	5.3	odd	4
1050.3.c.c.449.18		32	15.2	even	4
1050.3.e.d.701.5		16	5.4	even	2
1050.3.e.d.701.13		16	15.14	odd	2
1680.3.l.c.1121.9		16	4.3	odd	2
1680.3.l.c.1121.10		16	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-1.51079 + 2.59182i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.66538 - 2.13658i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(-4.43502 - 7.83139i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-1.51079 + 2.59182i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(-3.66538 - 2.13658i) q^{6} -2.64575 q^{7} -2.82843i q^{8} +(-4.43502 - 7.83139i) q^{9} -3.16228 q^{10} +14.6732i q^{11} +(3.02158 - 5.18363i) q^{12} -19.1112 q^{13} -3.74166i q^{14} +(-5.79548 - 3.37823i) q^{15} +4.00000 q^{16} -29.7911i q^{17} +(11.0753 - 6.27207i) q^{18} +14.7237 q^{19} -4.47214i q^{20} +(3.99718 - 6.85730i) q^{21} -20.7510 q^{22} -22.7912i q^{23} +(7.33076 + 4.27316i) q^{24} -5.00000 q^{25} -27.0273i q^{26} +(26.9979 + 0.336829i) q^{27} +5.29150 q^{28} +51.5923i q^{29} +(4.77754 - 8.19604i) q^{30} -38.6980 q^{31} +5.65685i q^{32} +(-38.0302 - 22.1681i) q^{33} +42.1310 q^{34} -5.91608i q^{35} +(8.87004 + 15.6628i) q^{36} -29.2081 q^{37} +20.8224i q^{38} +(28.8731 - 49.5328i) q^{39} +6.32456 q^{40} +28.6850i q^{41} +(9.69769 + 5.65286i) q^{42} -40.4802 q^{43} -29.3464i q^{44} +(17.5115 - 9.91701i) q^{45} +32.2317 q^{46} +10.5901i q^{47} +(-6.04316 + 10.3673i) q^{48} +7.00000 q^{49} -7.07107i q^{50} +(77.2131 + 45.0082i) q^{51} +38.2224 q^{52} +95.5975i q^{53} +(-0.476348 + 38.1808i) q^{54} -32.8102 q^{55} +7.48331i q^{56} +(-22.2444 + 38.1611i) q^{57} -72.9625 q^{58} -11.1354i q^{59} +(11.5910 + 6.75646i) q^{60} -104.131 q^{61} -54.7273i q^{62} +(11.7340 + 20.7199i) q^{63} -8.00000 q^{64} -42.7340i q^{65} +(31.3504 - 53.7828i) q^{66} +45.2575 q^{67} +59.5823i q^{68} +(59.0707 + 34.4328i) q^{69} +8.36660 q^{70} +93.7964i q^{71} +(-22.1505 + 12.5441i) q^{72} -62.8141 q^{73} -41.3066i q^{74} +(7.55396 - 12.9591i) q^{75} -29.4474 q^{76} -38.8216i q^{77} +(70.0499 + 40.8327i) q^{78} +122.486 q^{79} +8.94427i q^{80} +(-41.6612 + 69.4647i) q^{81} -40.5668 q^{82} +68.2772i q^{83} +(-7.99435 + 13.7146i) q^{84} +66.6150 q^{85} -57.2477i q^{86} +(-133.718 - 77.9452i) q^{87} +41.5020 q^{88} -79.4213i q^{89} +(14.0248 + 24.7650i) q^{90} +50.5635 q^{91} +45.5825i q^{92} +(58.4647 - 100.298i) q^{93} -14.9766 q^{94} +32.9231i q^{95} +(-14.6615 - 8.54632i) q^{96} -28.2049 q^{97} +9.89949i q^{98} +(114.911 - 65.0759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9	\( 16 q - 8 q^{3} - 32 q^{4} + 16 q^{6} - 4 q^{9} + 16 q^{12} - 20 q^{15} + 64 q^{16} - 32 q^{18} + 48 q^{19} + 28 q^{21} - 96 q^{22} - 32 q^{24} - 80 q^{25} + 64 q^{27} - 88 q^{33} + 160 q^{34} + 8 q^{36} + 80 q^{37} + 156 q^{39} - 336 q^{43} - 80 q^{45} + 32 q^{46} - 32 q^{48} + 112 q^{49} + 84 q^{51} - 32 q^{54} - 80 q^{55} - 264 q^{57} + 96 q^{58} + 40 q^{60} + 112 q^{61} + 112 q^{63} - 128 q^{64} + 240 q^{67} + 8 q^{69} + 64 q^{72} + 48 q^{73} + 40 q^{75} - 96 q^{76} + 208 q^{78} + 8 q^{79} - 124 q^{81} - 608 q^{82} - 56 q^{84} + 120 q^{85} - 120 q^{87} + 192 q^{88} + 160 q^{90} - 56 q^{91} + 104 q^{93} + 32 q^{94} + 64 q^{96} - 192 q^{97} - 52 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 32 * q^4 + 16 * q^6 - 4 * q^9 + 16 * q^12 - 20 * q^15 + 64 * q^16 - 32 * q^18 + 48 * q^19 + 28 * q^21 - 96 * q^22 - 32 * q^24 - 80 * q^25 + 64 * q^27 - 88 * q^33 + 160 * q^34 + 8 * q^36 + 80 * q^37 + 156 * q^39 - 336 * q^43 - 80 * q^45 + 32 * q^46 - 32 * q^48 + 112 * q^49 + 84 * q^51 - 32 * q^54 - 80 * q^55 - 264 * q^57 + 96 * q^58 + 40 * q^60 + 112 * q^61 + 112 * q^63 - 128 * q^64 + 240 * q^67 + 8 * q^69 + 64 * q^72 + 48 * q^73 + 40 * q^75 - 96 * q^76 + 208 * q^78 + 8 * q^79 - 124 * q^81 - 608 * q^82 - 56 * q^84 + 120 * q^85 - 120 * q^87 + 192 * q^88 + 160 * q^90 - 56 * q^91 + 104 * q^93 + 32 * q^94 + 64 * q^96 - 192 * q^97 - 52 * q^99

Introduction

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